CT technology has brought revolutionary impact on medical diagnosis and industrial nondestructive testing even since Hounsfield has invented the first CT machine in 1972, and CT has been one of the important detection measures in the industries of medical treatment, biology, aeronautics and astronautics, national defense, etc. X-ray cone-beam CT has been widely used in the fields of clinical medicine, security check, nondestructive detection, etc. Especially in medical and clinical diagnosis, spiral CT has been one of the indispensable measures for examination[1].
Although CT technology has currently achieved great success in the fields of industry, security check, medical care and so on, due to the complexity and the diversity of engineering application conditions, high requirements are put forth for further development of CT technology. In particular, in the industrial application, CT technology faces with many difficulties in terms of large-sized imaging with high accuracy and medical imaging with low dose, etc. This is mainly because: the CT scanning field of view (FOV) is restricted by the width of the X-ray beam, the size of the detector and the angle of the view, which gives rise to the possibility that the projection data of the scanning of a large object has truncations in the two directions of the detector and the scanning angle; the current mainstream CT algorithms are all overall reconstruction methods with respect to an intact object, which require the X-ray beam to cover the slices of the object completely and can hardly deal with the occasion where the projection data is truncated. Therefore, when imaging a large object or an irregular object, it is often difficult to perform the scanning directly, but instead, the ultimate image can only be reconstructed with approximate conversion methods such as data rearrangement after many times of scanning, which affects the speed and the accuracy of CT image adversely.
In addition, the detector of a CT device has been the key factor that influences the hardware cost of the CT device, and the price of the detector is directly proportional to the size and amount of the detector units. However, the price of detector remains high, which greatly limits the cost margin of CT products.
On the other hand, in medical CT imaging, in order to ensure that the projection data of the X-ray is not truncated, the width of the X-ray beam for use in the current CT scanning must cover the width of the slices of the human body, however, the real interest region often only relates to a certain organ of the human body, and as a result, an unnecessary radiation dose on the human body during the CT scanning is greatly increased. If the present way of CT design is not changed, the radiation dose can hardly be reduced. At present, medical irradiation has been the largest artificial ionizing radiation source for the human being, and hence reducing the X-ray dose during CT examination has become a significant subject concerning the health of the entire public and the posterities of the society.
Moreover, increasing requirements are put forth for the medical diagnosis. In particular, the medical diagnosis of some special body parts, such as female breast, cochlea, teeth and so on, requires high spatial resolution. In this regard, currently mainstream whole body spiral CT machine cannot meet the requirements for a normal medical diagnosis. With the rapid development of large-area flat-panel detector techniques, the medical flat-panel detector techniques have been mature enough for being applied in X-ray DR imaging with high spatial resolution. The flat-panel detector based on amorphous selenium and amorphous silicon techniques now has a detector aperture of larger than 500 mm×500 mm, and a pixel size of about 0.1 mm, whereas the detector of multilayered spiral CT has only a unit size of about 0.5 mm, so flat-panel detector can achieve CT images with much higher spatial resolutions compared with the spiral CT. However, due to the huge amount of data from the flat-panel detector, the data transmission speed still cannot meet the requirements for cone-beam CT imaging, and there are no CT devices using flat-panel detectors for whole body imaging in the practice. If we are not directed at the entire human body, but at the organs of interest with small-scaled flat-panel detectors to achieve CT imaging of the region of interest with high accuracy, it is possible that the technical bottleneck of slow data transmission could be broken.
With regard to the disadvantages and limitations of the CT system, we started to explore new CT imaging reconstruction methods and CT imaging modes. In fact, in many engineering applications, an overall CT imaging of the intact object is not required, but instead, only the imaging of the object in a certain region of interest (ROI) is needed. Especially in medical and clinical diagnosis, it is only necessary to image the part of the suspicious lesion[2].
At the beginning of the 1980s, the study of local CT imaging of an object has begun. Given the bondage of the CT reconstruction theories at that time, people could not precisely reconstruct the local CT image of the object, and hence resorted to a approximate function related to the slice image of the object. In 1985, Smith et al. proposed a local reconstruction algorithm of lambda tomography which reconstructs with the local projection data a function having the same singularity as the ROI density function[3]. Subsequently, Katsevich brought forward a local reconstruction algorithm of pseudolocal tomography which replaces the original function by reconstructing part of the Hilbert transform of the density function[4]. However, as these functions could not replace the real slice image of the object, they could hardly meet the requirements for real engineering applications, which greatly impaired the significance of local CT imaging in real engineering applications. Consequently, the study of local ROI imaging of an object had stagnated for a long term and could not find way out.
In the recent years, the CT reconstruction theory has witnessed huge progress. In 2002, Katsevich first put forth an exact reconstruction algorithm for cone-beam spiral CT based on the form of Filtered Back Projection (FBP). The algorithm solves well the problem of reconstructing long objects, and in case of projection data truncation in direction of the Z axis, it can still reconstruct the image of the object exactly for the scanned part. Besides, as the algorithm is in the form of FBP, it has considerable advantages over the iterative reconstruction algorithm in terms of reconstruction speed, so Katesevich provided a brand-new way of thinking for the development of CT algorithm[5-6]. In 2004, Zou and Pan brought forward an exact reconstruction algorithm for spiral CT in the form of Back Projection Filtration (BPF), which only requires theoretically minimum projection data to reconstruct the slice image of the object exactly[7-8]. Thus, the basic theoretical problems of spiral CT reconstruction have been solved appropriately. After that, the BPF algorithm has been widely applied to the CT image reconstruction of parallel beams, sector beams and cone beams. The BPF algorithm of Zou and Pan is a reconstruction algorithm based on the PI line, wherein the PI line is a line segment connecting any two points in the scanning trace, and wherein the BPF algorithm requires the two end points of each PI line to fall outside the support of the object. The greatest advantage of the algorithm lies in that the image in the PI line can still be reconstructed exactly when the projection data is somewhat truncated, which makes it possible to perform CT reconstruction with respect to the ROI instead of the intact object. In 2006, Defrise et al. obtained further achievements based on the BPF algorithm and eased the restriction of PI line by proving that when the PI line has only one end point outside the support of the object, the image in the PI line can still be reconstructed exactly with the projection data passing through the PI line[9]. In 2007, Wang et al. further proved that when the PI line completely falls within the object, the image of the object in the PI line can be reconstructed exactly with the truncated projection data if part of the image information in the PI line is known[10]. However, in real CT engineering applications, it is difficult to acquire information about the reconstruction values in the PI line inside the object in advance, so the method of Wang et al. has certain limitations in real applications.